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This video provides more examples and explanation about Law of Sines.

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Maths Tutorial: Trigonometry Law of Sines / Sine Rule

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For those of who want a more in-depth explanation of how Law of Sines is valid, you can watch the video below created by Khan academy

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Proof: Law of sines | Trig identities and examples | Trigonometry | Khan Academy

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Again, use the same equation from example 1, create an equation of 12/sin(110) = x/sin(50) where x is the missing b side length. Then cross multiply, you get 12*sin(50) = sin(110)x, and divide both sides by sin(110), then you get x = 16.7

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Using the equation derived from the law of sine, you can set up an equation like this: 15/sin(70) = x/sin(45) where x is the missing c side length. From there you will cross multiply and you will get an equation like this: 15*sin(45) = sin(70)x, then divide both sides by sin(70), and the x equals 11.3.

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Pythagorean Theorem is best used for solving right triangles, but when it comes down to solving other types of triangles, law of sine is more commonly applied. This padlet will explain how to use law of sine to solve a non-right triangle.

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The law of sine states that the proportion of length of triangle's side to the sin of its corresponding angle is the same for other two sides. Use the right triangle on the right as an example, you can create a list of proportion like this:
A: 10/sin(90) = 10
C: 6/sin(36.9) = 10
T: 8/sin(53.1) = 10
(If you get different answers, check if your calculator is in degree mode)

As you can see, all of the proportions equal to 10, therefore you can set up an equation like this:
a/sin(A) = c/sin(C) = t/sin(T) or more commonly known as a/sin(A) = b/sin(B) = c/sin(C)

This is the basic that you will utilize to solve more complicated problems(Remember this condition is the same for non-right triangle, too!)